OFFSET
1,1
COMMENTS
The old entry with this sequence number was a duplicate of A003687.
The answer to Kimberling's question is: yes. See the Bosma-Dekking-Steiner paper. - Michel Dekking, Oct 14 2018
LINKS
Muniru A Asiru, Table of n, a(n) for n = 1..5000
Wieb Bosma, Michel Dekking, Wolfgang Steiner, A remarkable sequence related to Pi and sqrt(2), arXiv 1710.01498 math.NT (2018).
Wieb Bosma, Michel Dekking, Wolfgang Steiner, A remarkable sequence related to Pi and sqrt(2), Integers, Electronic Journal of Combinatorial Number Theory 18A (2018), #A4.
FORMULA
Conjectures from Clark Kimberling, Aug 03 2022: (Start)
[a(n)*r] = n + [n*r] for n >= 1, where r = sqrt(2) and [ ] = floor.
MATHEMATICA
t = Nest[Flatten[# /. {0->{0, 1, 1}, 1->{0, 1}}] &, {0}, 5] (*A189687*)
f[n_] := t[[n]]
Flatten[Position[t, 0]] (* A086377 conjectured *)
Flatten[Position[t, 1]] (* A081477 conjectured *)
s[n_] := Sum[f[i], {i, 1, n}]; s[0] = 0;
Table[s[n], {n, 1, 120}] (*A189688*)
(* Clark Kimberling, Apr 25 2011 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Oct 12 2008
EXTENSIONS
Name corrected by Michel Dekking, Jan 04 2019
STATUS
approved